Answer to Question #6241 in Trigonometry for joy

Question

sin(x)^2=2cos(x)+2

Answer 1

Due to the famous identity cos²x+sin²x=1 therefore sin²x=1-cos²x
So sin²x=1-cos²x =2cos x+2
Let's denote cos x=t. We suppose that -1<=t<=1
So we get the equation:
1-t^2=2t+2
t^2+2t+1=0
(t+1)^2=0
t=-1
So cos x=-1
x=pi+2k pi where k - integer

Also we created video where this particular problem is considered. Please take a look!